The Intensity of Transmitted Light* 169 



to be uniformly distributed. A similar result might have 

 been obtained from a consideration of the differential 

 equation, for if we make ^=0 in (15), we obtain the result, 



-^ = (48) 



of which the integral is 



p = <j>(t) + xl^(x); (49) 



if we now apply the conditions / = ^, when x=o, and 



P 



initially, we find for the value of (/), and 



P 



for the value of \p(x). 



The next case that I shall consider, is when d = ; and 

 first it may be remarked that this condition implies m = Of 

 and therefore implies that the body A by the absorption 

 of light is converted into a body B which is perfectly 

 transparent. We are, as far as I am aware, acquainted 

 with no form of matter which is perfectly transparent, so 

 that the investigation might not be strictly applicable to 

 actual experience, but it is well known that the action of 

 light on many organic colours is of such a nature as to 

 discharge the colour ; to such cases the present investiga- 

 tion will apply approximately; making 3 = in (15) we 

 obtain 



dxdt dx 



Integrating with respect / x and adding an arbitrary 

 function of /, we obtain 



dp a 



to integrate a second time, substitute U for £^<= ; also since 

 when m~0,c takes the value— /x, let this value be used, 

 then we obtain 



